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Nov 27, 2019 at 22:58 comment added Iosif Pinelis Interesting! It would probably have never occurred to me that simply bounding the harmonic mean (of the arithmetic means) by the corresponding arithmetic mean would work, even for even $n$. However, after that, you are only rewriting the bound on the difference, and I don't see how this could be made work for odd $n$.
Nov 27, 2019 at 20:14 history answered Luis Ferroni CC BY-SA 4.0